I wouldn't reccomend doing the Statue Race single handed on a 16 or 18. At 200 pounds, you likely would not be able to right the boat alone.
The race is in the middle of NY Harbor with the threat of barges, ferries, and etc crossing your path. You don't want to capsize and not be able to right your boat in their path. Not to mention the main stretch of the race is open water, there is a possibility of you being swept out to sea.
I am not deterring you from this race by any means, it's a great race, i've done it the last 5 years without any problems.
I'd highly reccomend to find a lightweight crew or if you are totally new at sailing, try to crew for someone the first time in this race.
SHBCC might not even let you race solo without proving you can right your boat especially after this past year's events.